Problem: You have $6$ reindeer, Rudy, Jebediah, Ezekiel, Lancer, Gloopin, and Balthazar, and you want to have $5$ fly your sleigh. You always have your reindeer fly in a single-file line. How many different ways can you arrange your reindeer?
Answer: We can build our line of reindeer one by one: there are $5$ slots, and we have $6$ different reindeer we can put in the first slot. Once we fill the first slot, we only have $5$ reindeer left, so we only have $5$ choices for the second slot. So far, there are $6 \cdot 5 = 30$ unique choices we can make. We can continue in this way for the third reindeer, and so on, until we reach the last slot, where we will have $2$ choices for the last reindeer. So, the total number of unique choices we could make to get to an arrangement of reindeer is $6\cdot5\cdot4\cdot3\cdot2$. Another way of writing this is $\dfrac{6!}{(6-5)!} = 720$